Electrical Power Systems
Today's heavily loaded and stressed power transmission networks exhibit very complex dynamic behavior, when subjected to small or large disturbances. Power system dynamic behavior under stressed (e.g. heavy load) operating conditions is in this project analyzed using normal forms of vector fields. This technique obtains nonlinear corrections to the linear behavior through normal form analysis. This second order analysis has provided insight into real power network dynamic problems associated with interaction of control nodes, system separation, and effect of nonlinear elements like HVDC (=High Voltage Direct Current) that were not obvious from linear analysis.
The project team applies the Normal Forms of Vector Fields to a 50-generator IEEE test system, a 11-generator system and a 4-generator system. The team used the 50-generator system for analyzing and predicting interarea separation and analyzing the effect of control interaction on system performance. The 11-generator system was used to analyze the effect of stress on the stability boundary and on the invariant manifolds. The 4-generator system was used to study the effect of HVDC on modal interaction. The figures above show a crucial part of the 50-generator system and the response of this system after a fault for different control settings. The stable response is obtained by controller gain tuning using nonlinear techniques. (Supported by NSF, EPRI.)
- Collaborators
- Dr. Vijay Vittal (principle investigator), Department of Electrical and Computer Engineering, Iowa State University.
- Recent Publications
- Papers, refeered
- Lin, C.-M., V. Vittal, W. Kliemann, and A. A. Fouad, Investigation of modal interaction and
its effects on control performance in stressed power systems using normal forms of vector fields,
to appear in IEEE Transactions on PWRS, Paper # 95SM522-3.
- Treinen, R., V. Vittal, and W. Kliemann, An improved technique to determine the controlling
unstable equilibrium point in a power system, IEEE Transactions on CS 43(1996), 313-323.
- Ni, Y.-X., V. Vittal, W. Kliemann, and A. A. Fouad, Nonlinear modal interaction in HVDC/AC
power systems with DC power modulation, to appear in IEEE Transactions on PWRS, Paper
#96WM276-6.
- Saha, S. A. A. Fouad, W. Kliemann, and V. Vittal, Stability boundary approximation of a power
system using the real norm of vector fields, to appear in IEEE Transactions on PWRS, Paper #
96SM503-3.
- Thapar, J., V. Vittal, W. Kliemann, and A. A. Fouad, Application of the normal form of vector
fields to predict interarea separation in power systems, to appear in IEEE Transactions on PWRS,
Paper #96SM517-3.
- Papers, not refereed
- Vittal, V., W. Kliemann, S. K. Starrett, and A. A. Fouad, Analysis of stressed power systems
using normal forms, in: Proceedings of the International Symposium on Circuits and Systems
(ISCAS 92), San Diego (1992), 2553-2556.
- Starrett, S., W. Kliemann, V. Vittal, and A. A. Fouad, Power system modal behavior:
Significance of second and third order nonlinear terms, in: Proceedings of the 25th North
American Power Symposium, Washington D. C., (1993), 246-255.
- Starrett, S. K., V. Vittal, W. Kliemann, and A. A. Fouad, A methodology for the analysis of
nonlinear interarea interactions between power system natrual modes of oscillation utilizing
normal forms of vector fields, Proceedings of the 1993 International Symposium on Nonlinear
Theory and its Applications, Hawaii (1993), 523-538.
- Fouad, A. A., V. Vittal, and W. Kliemann, Analysis of stressed interconnected power networks,
EPRI Report (1993), 95 pp.
- Lin, C.-M., W. Kliemann, V. Vittal, and A. A. Fouad, Interaction between excitation control
modes and inertial modes in stressed power systems, in: Proceedings ofthe 26th North American
Power Symposium (1994), 669-678.
- Starrett, S. K., V. Vittal, W. Kliemann, and A. A. Fouad, Excitation of second-order normal
forms and first-order Jordan forms modes of oscillation, in: Proceedings of the 26th North
American Power Symposium, (1994), 27-36.
- Saha, S., V. Vittal, W. Kliemann, and A. A. Fouad, Local approximation of stability boundary
of a power system using the real normal form of vector fields,in Proceedings of the International
Symposium on Circuits and Systems (ISCAS 95), (1995), 2330-2333.
- Lin, S., V. Ajjarapu, B. Lee, V. Vittal, and W. Kliemann, Control of voltage collapse in an
electrical power system using center manifold theory, in: Proceedings of the Midwest Power
Symposium 95, 4 pp.
- Ni, Y-X., V. Vittal, W. Kliemann, and A. A. Fouad, Application of normal form of vector fields
to AC/DC power systems, in: Proceedings of the 27th North American Power Symposium
(1995), 6-12.
- Saha, S., W. Kliemann, V. Vittal, and A. A. Fouad, Effect of stress on the boundary of stability
of a power system, Proceedings of the 27th North American Power Symposium (1995), 257-262.
- Ni, Y.-X., V. Vittal and W. Kliemann, System trajectory in the neighborhood of the controlling
UEP viewed from decouped modal space via normal form of vector fields, Proceedings of the 28th
North American Power Symposium (1996), 8 pp.